What if?

Cap11: Why model?

Grupo top de IC

UnB

Capítulo 11

  • Part I conceitual, estimadores não paramétricos

  • Part II dados “reais”, estimadores paramétricos

  • We define nonparametric estimators: those that produce estimates from the data without any a priori restrictions on the conditional mean function: Part I

  • Parametric estimation and other approaches to borrow information are our only hope when data are unable to speak for themselves.

Data cannot speak for themselves

  • 16 individuals infected with HIV randomly sampled from a larger target population.

  • Each individual receives a certain level of antiretroviral therapy. At the end CD4 cell count, in cells/mm3 is measured: We wish to consistently estimate the mean of cell counts for individuals with level A=a.

\(\hat{E}=[Y|A=a]\) é um estimador consistente.

Tratamentos

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   10.0    27.5    60.0    67.5    87.5   170.0 
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   50.0   105.0   160.0   146.2   185.0   220.0

  • Quanto é a predição para A=90?

Parametric estimators of the conditional mean

\(E[Y|A]= \theta_0 + \theta_1A\)

  • modelo linear, \(\theta\) são parâmetros.

[1] 216.89
  • A certain degree of model misspecification is almost always expected.

Mais parametros

[1] 197.1269

  • Often modeling can be viewed as a procedure to transform noisy data into more or less smooth curves.

The bias-variance trade-off

Qual o certo?

[1] "216.89 IC = 172.1 - 261.6)"
[1] "197.13 IC = 142.8 - 251.5)"
  • Acabou!